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Simplifying 10x2 + 17x + -42 = 0 Reorder the terms: -42 + 17x + 10x2 = 0 Solving -42 + 17x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -4.2 + 1.7x + x2 = 0 Move the constant term to the right: Add '4.2' to each side of the equation. -4.2 + 1.7x + 4.2 + x2 = 0 + 4.2 Reorder the terms: -4.2 + 4.2 + 1.7x + x2 = 0 + 4.2 Combine like terms: -4.2 + 4.2 = 0.0 0.0 + 1.7x + x2 = 0 + 4.2 1.7x + x2 = 0 + 4.2 Combine like terms: 0 + 4.2 = 4.2 1.7x + x2 = 4.2 The x term is 1.7x. Take half its coefficient (0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. 1.7x + 0.7225 + x2 = 4.2 + 0.7225 Reorder the terms: 0.7225 + 1.7x + x2 = 4.2 + 0.7225 Combine like terms: 4.2 + 0.7225 = 4.9225 0.7225 + 1.7x + x2 = 4.9225 Factor a perfect square on the left side: (x + 0.85)(x + 0.85) = 4.9225 Calculate the square root of the right side: 2.218670773 Break this problem into two subproblems by setting (x + 0.85) equal to 2.218670773 and -2.218670773.Subproblem 1
x + 0.85 = 2.218670773 Simplifying x + 0.85 = 2.218670773 Reorder the terms: 0.85 + x = 2.218670773 Solving 0.85 + x = 2.218670773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = 2.218670773 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = 2.218670773 + -0.85 x = 2.218670773 + -0.85 Combine like terms: 2.218670773 + -0.85 = 1.368670773 x = 1.368670773 Simplifying x = 1.368670773Subproblem 2
x + 0.85 = -2.218670773 Simplifying x + 0.85 = -2.218670773 Reorder the terms: 0.85 + x = -2.218670773 Solving 0.85 + x = -2.218670773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.85' to each side of the equation. 0.85 + -0.85 + x = -2.218670773 + -0.85 Combine like terms: 0.85 + -0.85 = 0.00 0.00 + x = -2.218670773 + -0.85 x = -2.218670773 + -0.85 Combine like terms: -2.218670773 + -0.85 = -3.068670773 x = -3.068670773 Simplifying x = -3.068670773Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.368670773, -3.068670773}
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